Example Questions

Example Question #1 : Radioactive Decay Equations

Over the past few years, the number of students enrolled at a certain university has been decreasing. Each year there is a 12% decrease in student enrollement. Currently, 14,286 students are enrolled. If this trend continues, how many students will be enrolled in 5 years?

Possible Answers:

Correct answer:

Explanation:

This is an exponential decay problem. The formula for exponential decay is:

Where

= future value

= present value

= rate of decay

= number of periods

This problem requests the number of students five years in the future. The rate of decay is twelve percent. Therefore:

Example Question #2 : Radioactive Decay Equations

Sceintists recently discovered a new type of metal compound. They have roughly 15 grams of this compound, which has a half life of 16 hours. Approximately how much of this substance will the scientists have in 24 hours?

Example Question #4 : Radioactive Decay Equations

The number of butterflies in an exhibit is decreasing with an exponential decay. The number of butterflies is decreasing by every year. There are butterflies in the exhibit right now. How many butterflies will be in the exhibit in years?

Possible Answers:

Correct answer:

Explanation:

Because the butterflies are decreasing exponentially, we can use this equation

Example Question #1 : Radioactive Decay Equations

The number of fish in an aquarium is decreasing with exponential decay. The population of fish is decreasing by each year. There are fish in the aquarium today. If the decay continues how many fish will be in the aquarium in years?

Possible Answers:

None of these answers are correct

Correct answer:

Explanation:

Every year the population of fish losses 7%. In other words, every year 93% of the fish remain from the previous year. Knowing this, we can use the original number of fish to find the number of fish for the next year. Since we want to know the number of fish 4 years from now, we multiply 1500 by 93% four times.

Example Question #9 : Radioactive Decay Equations

A school is losing a certain number of students each year. This year, the school has students. Four years ago the school had students. The yearly rate of the school losing students has been the same for the last four years. What is the school's yearly rate of losing students?

Possible Answers:

Correct answer:

Explanation:

This is an exponential decay problem, meaning that the decay of the school's students can be found using

is the number of students currently at the school, which is 242

is the number of students that were at the school 4 years ago, which is 591

is the number of times the decay has occurred. Since, we are trying to find the yearly decay, the decay that happened to the school from one year to the next, and we have the number of students from 4 years ago, .

is the decay rate of the school that we are trying to find. Because we have every number except for , we can plug the values into the equation to solve for .

Example Question #10 : Radioactive Decay Equations

Cells in a dish have started to decay. The cells are decaying by every minutes. When you left the cells there were cells in the dish. Now there are cells in the dish. Approximately how long did you leave the cells for?

Possible Answers:

Correct answer:

Explanation:

This is an exponential decay problem. That means that after 20 minutes 3% of the cells decay and 97% of the cells in the dish are left. To find the new amount of cells in the dish, we multiple the original number by the 97%.

The number of cells after every 20 minute interval can be calculated this way. Therefore, to find how long the cell were decaying we use,

Which can be rewritten as,

Now we can solve for , which is the amount of time that you were gone

To solve for , we must take the log of both sides to base 10. This will give us,

Remember! is the number of decays that the cells went through. Each decay took 20 minutes to get through, however.

All Algebra II Resources

Report an issue with this question

If you've found an issue with this question, please let us know. With the help of the community we can continue to
improve our educational resources.

Do not fill in this field

* Your Name:

* Your Email:

* Issue Description:

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one
or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing
the
information described below to the designated agent listed below. If Varsity Tutors takes action in response to
an
Infringement Notice, it will make a good faith attempt to contact the party that made such content available by
means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such
as
ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially
misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located
on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf;
An identification of the copyright claimed to have been infringed;
A description of the nature and exact location of the content that you claim to infringe your copyright, in \
sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require
a
link to the specific question (not just the name of the question) that contains the content and a description of
which specific portion of the question – an image, a link, the text, etc – your complaint refers to;
Your name, address, telephone number and email address; and
A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe
your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the
information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are
either the copyright owner or a person authorized to act on their behalf.